One of the best ways security experts say you can protect yourself besides changing your password is setting your accounts up for two-step verification. For example, Facebook calls it code generator.
First, you have to change your password by going to the lock symbol on the upper right hand corner of the screen. One problem is every website calls it something different.
When you're there, click general, you find it under the Facebook "F," then you are able to change your password.
Once complete, click on security, then select "code generator" and follow the steps.
Which passwords do you need to change because of the bug? Click here for a list.